Randomize the radius of a curve
To do it manually, in edit mode use L to select linked points and adjust the radius property which will be applied to all selected points. The radius property can be found in the properties sidebar N.



Or you can automate it with python. A curve object can have multiple splines, each spline then has multiple points. Note that bezier curves and nurbs curves use different property names for the points. For bezier curves it is bezier_points while nurbs curves use points.

import bpy
import random

c_obj = bpy.data.objects['BezierCurve']

for s in c_obj.data.splines:
    spl_rad = random.random()
    # change to s.points for nurbs curves
    for p in s.bezier_points:
        p.radius = spl_rad